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Analytical solution for coupled partial differential equations

  1. Aug 6, 2012 #1

    In my study i came across to solve the analytical solution for coupled equation y(x,t) and z(x,t).The equations contains" f " function which is a function of the first variable exponentially.

    The first equation is : ∂y/∂t=∂^2(y)/∂x^2- 2*f(y)*z;
    The second equation : ∂z/∂t=∂^2(z)/∂x^2-f(y)*z;.

    and f is correlated with y exponentially e.g. f=exp(1/y).I have to solve for any type of boundary conditions. I have got a problem in finding the coupled solution. Can any one please help me to start this problem?

    Thanks in advance.
  2. jcsd
  3. Aug 6, 2012 #2


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    It looks like if you multiply the second equation by -2 and add it to the first equation you will get a simpler equation for y - 2z. You can use the result to eliminate, say, z in one of the equations and get a single equation for y.
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